A note on the occurrence of the illusory between-person component in the random intercept cross-lagged panel model

The random intercept cross-lagged panel model (RICLPM) decomposes longitudinal associations between two processes X and Y into stable between-person associations and temporal within-person changes. In a recent study, Bailey et al. demonstrated through a simulation study that the between-person variance components in the RICLPM can occur only due to the presence of time-varying covariate processes that are omitted from the analysis model. Therefore, the between-person component was termed illusory. In this article, necessary and sufficient conditions for the occurrence of such illusory between-person components in an RICLPM are analytically derived and systematically investigated in a simulation study.